How does a marginal increase in t affect welfare

Question

Problem

Social security in the Diamond model. Consider a Diamond economy where g is zero, production is Cobb-Douglas, and utility is logarithmic.

a. Social security in the Diamond model. Consider a Diamond economy where g is zero, production is Cobb-Douglas, and utility is logarithmic.

(i) How, if at all, does this change affect equation (2.60) giving kt +1 as a function of k_t?

(ii) How, if at all, does this change affect the balanced-growth-path value of k?

(iii) If the economy is initially on a balanced growth path that is dynamically efficient, how does a marginal increase in T affect the welfare of current and future generations? What happens if the initial balanced growth path is dynamically inefficient?

(b) Fully funded social security. Suppose the government taxes each young person an amount T and uses the proceeds to purchase capital. Individuals born at t therefore receive (1 + r_t+1)T when they are old.

(i) How, if at all, does this change affect equation (2.60) giving kt +1 as a function of k_t?

(ii) How, if at all, does this change affect the balanced-growth-path value of k?

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.